Whether or not "Mother may I" is a problem - you think it is by definition, I think @hawkeyefan agrees with you, I know @Ovinomancer doesn't - I think that it does flow, in part at least, from features of system. I'll explain why by reference to this post:It is not really productive to lay this issue at any one person’s feet. MMI is not a player or a dm problem or a system problem.
In this post, overgeeked is describing a system in which all the players can do is establish truths about their PCs' intents and bodily motions, and make suggestions about what, in the fiction, might follow from that. The GM has all the authority to decide what actually happens as a result of a PC intending something and trying to move their body so as to accomplish it.Importantly, the three-step play loop you present is slightly off. The version in the PHB is this:
1. The DM describes the environment.
2. The players describe what they want to do.
3. The DM narrates the results of the adventurers' actions.
A further bit of explanatory text for #2 is enlightening: "the DM listens to every player and decides how to resolve those actions. Sometimes, resolving a task is easy. If an adventurer wants to walk across a room and open a door, the DM might just say that the door opens and describe what lies beyond. But the door might be locked, the floor might hide a deadly trap, or some other circumstance might make it challenging for an adventurer to complete a task. In those cases, the DM decides what happens, often relying on the roll of a die to determine the results of an action."
So it's rather explicit that the player gets to make a declaration of intent, i.e. describe what they want their character to do (#2), but have no control over the outcome of that attempted action because the DM narrates the results of the adventurers' actions (#3).
A lot of the MMI examples provided in the thread sound like the player wanting to not only describe their character's attempted action (#2) but also narrate the outcome (#3)
That is a system which is ripe with potential for "Mother may I" as a problem, and which - on @Ovinomancer's account - literally exemplifies "Mother may I" whether or not it causes problems at the table.
We could contrast it with a system in which players do have some control over the outcomes that result from what their PCs intend and how their PCs move their bodies. For instance, where the GM's job is to set a difficulty, the player is then able to draw on various player-side capabilities and resources, a resulting dice roll is made, and if that roll succeeds then what the player wanted becomes true in the fiction. (Burning Wheel is a RPG with the clearest statement of this sort of system that I know. 4e D&D skill challenges work like this too, at least as I read the rulebook.)
In the sort of alternative system, there is still some scope for "Mother may I", because it will be the role of the GM to understand and mechanically frame the player's declared action within the established fiction. But clearly that scope is much reduced, compared to a system in which the GM literally has all the say over outcomes.
And of course there are possible systems other than the two I've mentioned so far that also make a difference: for instance, Apocalypse World's "If you do it, you do it" means that when the fiction includes a certain thing, then the dice have to be rolled and the result of that roll imposes various obligations and confers various permissions on the game participants to establish new bits of fiction. The need for that initial adjudication of the fiction once again creates some scope for "Mother may I", but not a lot - it will generally be clear to everyone when a character is "doing it", given the way the system defines the its.
It's obviously not an objection to a system that it creates more (or less) scope for "Mother may I" than some other system, but I think it is a feature that can be worth noting.